Differential calculus and equations Books

The 1960s were perhaps a decade of confusion, when scientists faced d- culties in dealing with imprecise information and complex dynamics. A new set theory and then an in?nite-valued logic of Lot? A. Zadeh were so c- fusing...

The aim of this book is to present different aspects of the deep interplay between Partial Differential Equations and Geometry. It gives an overview of some of the themes of recent research in the field and their mutual links, describing the main...

This book is devoted to the study of positive solutions to indefinite problems. The monograph intelligibly provides an extensive overview of topological methods and introduces new ideas and results. Sticking to the one-dimensional setting, the author...

1.Preliminaries on Hilbert spaces.- 2.Operators in Hilbert spaces.- 3.The semilinear problem.- 4.The topological degree.- 5.Nonresonance and topological degree.- 6.Playing around resonance.- 7.The variational method.- 8.At resonance, again.- 9...

This research monograph brings together, for the first time, the varied literature on Yosida approximations of stochastic differential equations (SDEs) in infinite dimensions and their applications into a single cohesive work. The author provides a clear...

Now in its second edition, this monograph explores the Monge-Ampère equation and the latest advances in its study and applications.  It provides an essentially self-contained systematic exposition of the theory of weak solutions, including...

This book provides a comprehensive advanced multi-linear algebra course based on the concept of Hasse-Schmidt derivations on a Grassmann algebra (an analogue of the Taylor expansion for real-valued functions), and shows how this notion provides a natural...

In the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content describing and analysing classical and modern methods with emphasis on the algebraic structure of linear...

Preliminaries.- Function Systems.- Shannon Sampling Variants.- Bandlimited Sampling.- Spline Sampling.- Bandlimited Fourier Expansion Sampling.- Spacelimited Multi-Scale Approximate Identity Sampling.- Spacelimited...

Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed problems-involved in a numerous mathematical models in physics, engineering, and finance- can be approached in a variety of ways. Historically, there have been three...

Extremality results proved in this Monograph for an abstract operator equation provide the theoretical framework for developing new methods that allow the treatment of a variety of discontinuous initial and boundary value problems for both ordinary and...

This accessible monograph is devoted to a rapidly developing area on the research of qualitative theory of fractional ordinary differential equations and evolution equations. It is self-contained and unified in presentation, and provides the readers the...

This book has been considered by academicians and scholars of great significance and value to literature. This forms a part of the knowledge base for future generations. So that the book is never forgotten we have represented this book in a print format...

Grade 9 was the most boring year of my life. I remember sitting in front of a map, trying to memorize the names and locations of all the eighty-five Mexican rivers. I sat there, fearing the exam where I would have to face an empty map of Mexico, and I...

Ever since the groundbreaking work of J.J. Kohn in the early 1960s, there has been a significant interaction between the theory of partial differential equations and the function theory of several complex variables. Partial Differential Equations and...

Examines developments in the oscillatory and nonoscillatory properties of solutions for functional differential equations, presenting basic oscillation theory as well as recent results. The book shows how to extend the techniques for boundary value...

This work thoroughly covers the concepts and main results of probability theory, from its fundamental principles to advanced applications. This edition provides examples early in the text of practical problems such as the safety of a piece of engineering...

"Provides a thorough introduction to the algebraic theory of systems of differential equations, as developed by the Japanese school of M. Sato and his colleagues. Features a complete review of hyperfunction-microfunction theory and the theory of...

Preface. Linear Partial Differential Equations with Multiple Involutive Characteristics; O. Liess, L. Rodino. Gevrey and Analytic Hypoellipticity; D.S. Tartakoff. Higher Microlocalization and Propagation of Singularities; O. Liess. Conormality and...

Preface; E.M. de Jager. Part I: Invited Plenary Lectures. Integrability, Computation and Applications; M.J. Ablowitz, S. Chakravarty, B. M. Herbst. Applications of KdV; D.G. Crighton. Instructive History of the Quantum Inverse Scattering Method; L...

Preface. Part One: Survey Papers. Degenerate Parabolic and Elliptic Equations; Yazhe Chen. Nonlinear Hyperbolic Conservation Laws; Xiaxi Ding, Tong Zhang. Elliptic and Parabolic Equations; Guangcang Dong. Viscosity Solutions of Fully Nonlinear...

A NATO Advanced Research Workshop on Classical and Modern Potential The­ ory and Applications was held at the Chateau de Bonas, France, during the last week of July 1993. The workshop was organized by the Co-Directors M...

ICPT91, the International Conference on Potential Theory, was held in Amersfoort, the Netherlands, from August 18--24, 1991. The volume consists of two parts, the first of which contains papers which also appear in the...

This volume contains the proceedings of the NATO Advanced Research Workshop on "Asymptotic-induced Numerical Methods for Partial Differ­ ential Equations, Critical Parameters, and Domain Decomposition," held at Beaune (France),...

This volume is devoted to integral inequalities of the Gronwall-Bellman-Bihari type. Following a systematic exposition of linear and nonlinear inequalities, attention is paid to analogues including integro-differential...

'Et moi, ... , si j'avait so comment CD revenir. je One service mathematics bas rendered !be human race. It bas put common sense back n 'y semis point aile.' JulesVeme where it belongs, on !be topmost shelf next to !be dusty...

4Et moi, ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty...

2 The authors of these issues involve not only mathematicians, but also speci­ alists in (mathematical) physics and computer sciences. So here the reader will find different points of view and approaches to the considered field...

Frechet spaces have been studied since the days of Banach. These spaces, their inductive limits and their duals played a prominent role in the development of the theory of locally convex spaces. Also they are natural tools in...

This book contains about 3000 first-order partial differential equations with solutions. New exact solutions to linear and nonlinear equations are included. The text pays special attention to equations of the general form, showing their dependence upon...

This book is intended to be used as a rather informal, and surely not complete, textbook on the subjects indicated in the title. It collects my Lecture Notes held during three academic years at the University of Siena for a one semester course on "Basic...

Existence Proofs For Ordinary Differential Equations Of The First Order And Degree is a book written by Edwin Raymond Smith in 1908. The book is a comprehensive study of ordinary differential equations of the first order and degree, and provides a...

Compressible Flow with Application to Shocks and Propulsion is part of the series "Mathematics and Physics for Science and Technology", which combines rigorous mathematics with general physical principles to model practical engineering systems with a...

Vector Fields with Applications to Thermodynamics and Irreversibility is part of the series "Mathematics and Physics for Science and Technology", which combines rigorous mathematics with general physical principles to model practical engineering systems...

CR Manifolds and the Tangential Cauchy Riemann Complex provides an elementary introduction to CR manifolds and the tangential Cauchy-Riemann Complex and presents some of the most important recent developments in the field. The first half of the book...

1 Introduction.- Part I: Basic Solutions.- 2 Function Spaces and the First Renormalized Functional.- 3 The Simplest Heteroclinics.- 4 Heteroclinics in x1 and x2.- 5 More Basic Solutions.- Part II: Shadowing Results.- 6 The Simplest Cases.- 7 The Proof of...

Many problems in mathematical physics rely heavily on the use of elliptical partial differential equations, and boundary integral methods play a significant role in solving these equations. Stationary Oscillations of Elastic...

Notation.- Preliminaries.- Some Fixed Point Theorems.- Local and Global Inversion Theorems.- Leray-Schauder Topological Degree.- An Outline of Critical Points.- Bifurcation Theory.- Elliptic Problems and Functional Analysis.- Problems with A Priori...

The second in a series of three volumes that survey the theory of theta functions, this volume emphasizes the special properties of the theta functions associated with compact Riemann surfaces and how they lead to solutions of...

* Presented from a geometric analytical viewpoint, this work addresses advanced topics in complex analysis that verge on modern areas of research * Methodically designed with individual chapters containing a rich collection of...

This book presents the mathematical study of vortices of the two-dimensional Ginzburg-Landau model, an important phenomenological model used to describe superconductivity. The vortices, identified as quantized amounts of...

This four-part text beautifully interweaves theory and applications in Fuchsian Reduction. Background results in weighted Sobolev and Holder spaces as well as Nash-Moser implicit function theorem are provided. Most chapters...

This work will serve as an excellent first course in modern analysis. The main focus is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type...

Kuo-Tsai Chen (1923-1987) is best known to the mathematics community for his work on iterated integrals and power series connections in conjunction with his research on the cohomology of loop spaces. His work is intimately...

The last fifty years have witnessed several monographs and hundreds of research articles on the theory, constructive methods and wide spectrum of applications of boundary value problems for ordinary differential equations. In...